Boyfriend advice ?

I have been dating someone for over a year and there are some things that bother me and sometimes I remember them and I feel I take it out on him. We have fun, we go out, we occupy each other’s entire weekends but he expects me not to communicate with any males but I see him messaging females from high school.  I have already made it known about a specific individual but he keeps talking to her and commenting on her Instagram stories is there a problem with me? Am I the problem? I saw him on snap with a female and then he lied and told me he was replying to an insta story. What can I do? I don’t want to be lied to I want the same respect. But I know I’m bothered and upset by this. Am I in the wrong ?